12n
0695
(K12n
0695
)
A knot diagram
1
Linearized knot diagam
4 5 9 2 11 9 12 3 6 1 8 6
Solving Sequence
3,9
4
8,12
7 6 10 1 11 5 2
c
3
c
8
c
7
c
6
c
9
c
12
c
11
c
5
c
2
c
1
, c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.13964 × 10
33
u
26
− 5.99682 × 10
33
u
25
+ ··· + 3.81255 × 10
34
b − 2.47902 × 10
35
,
− 2.08631 × 10
34
u
26
− 1.00367 × 10
35
u
25
+ ··· + 7.62510 × 10
34
a − 4.15461 × 10
36
,
u
27
+ 5u
26
+ ··· + 400u + 64i
I
u
2
= h176363u
14
+ 128033u
13
+ ··· + 74749b − 928241, 61025u
14
+ 17351u
13
+ ··· + 74749a − 408316,
u
15
− 3u
13
+ 4u
11
− 2u
10
+ u
9
+ 5u
8
− 5u
7
− 5u
6
− u
5
+ 9u
4
+ 9u
3
− 4u
2
− 3u + 1i
I
u
3
= h4u
7
− 2u
6
− 6u
5
+ u
2
ba + 6u
4
+ 8u
3
+ b
2
− 2ba − au − 5u
2
− 4u + 7,
− u
7
a + u
6
a − 2u
7
+ u
5
a + u
6
− 2u
4
a + 3u
5
− u
3
a − 3u
4
+ 2u
2
a − 4u
3
+ a
2
+ 3u
2
− 2a + 2u − 4,
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
I
v
1
= ha, 4b − v + 4, v
2
− 6v + 4i
* 4 irreducible components of dim
C
= 0, with total 76 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−1.14 × 10
33
u
26
− 6.00 × 10
33
u
25
+ · · · + 3.81 × 10
34
b − 2.48 ×
10
35
, −2.09 × 10
34
u
26
− 1.00 × 10
35
u
25
+ · · · + 7.63 × 10
34
a − 4.15 ×
10
36
, u
27
+ 5u
26
+ · · · + 400u + 64i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
a
12
=
0.273610u
26
+ 1.31627u
25
+ ··· + 187.951u + 54.4860
0.0298919u
26
+ 0.157291u
25
+ ··· + 24.8662u + 6.50226
a
7
=
0.603225u
26
+ 2.76296u
25
+ ··· + 357.964u + 98.6342
−0.0171631u
26
− 0.0712776u
25
+ ··· − 6.60142u − 2.12730
a
6
=
0.603225u
26
+ 2.76296u
25
+ ··· + 357.964u + 98.6342
0.106750u
26
+ 0.472111u
25
+ ··· + 56.0584u + 14.0753
a
10
=
−1.39047u
26
− 6.44135u
25
+ ··· − 854.422u − 239.806
−0.0213532u
26
− 0.118447u
25
+ ··· − 20.2449u − 6.81187
a
1
=
−1.11686u
26
− 5.12508u
25
+ ··· − 666.471u − 185.320
0.00853870u
26
+ 0.0388446u
25
+ ··· + 3.62131u − 0.309612
a
11
=
0.266493u
26
+ 1.31042u
25
+ ··· + 196.198u + 58.3012
0.0227747u
26
+ 0.151445u
25
+ ··· + 33.1133u + 10.3175
a
5
=
1.34575u
26
+ 6.12897u
25
+ ··· + 782.304u + 214.401
0.228884u
26
+ 1.00389u
25
+ ··· + 115.833u + 29.0810
a
2
=
−1.34575u
26
− 6.12897u
25
+ ··· − 782.304u − 214.401
−0.0973818u
26
− 0.399745u
25
+ ··· − 37.9426u − 9.30362
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.27815u
26
− 5.86437u
25
+ ··· − 764.039u − 222.235
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
27
− 3u
26
+ ··· − 36u + 16
c
3
, c
8
u
27
+ 5u
26
+ ··· + 400u + 64
c
5
, c
7
, c
11
u
27
+ u
26
+ ··· − 5u − 1
c
6
, c
9
, c
12
u
27
− 25u
25
+ ··· + 6u + 1
c
10
u
27
+ 19u
26
+ ··· − 768u + 256
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
27
− 23y
26
+ ··· − 2192y −256
c
3
, c
8
y
27
− 9y
26
+ ··· + 49920y −4096
c
5
, c
7
, c
11
y
27
+ 5y
26
+ ··· + 15y −1
c
6
, c
9
, c
12
y
27
− 50y
26
+ ··· + 68y −1
c
10
y
27
− 19y
26
+ ··· + 5636096y −65536
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.03853
a = −1.40893
b = −0.426622
−2.58509 −5.21480
u = −1.162780 + 0.105322I
a = 0.256922 + 0.751420I
b = −0.008028 + 1.317420I
−2.12887 + 0.87840I −1.69411 + 0.10409I
u = −1.162780 − 0.105322I
a = 0.256922 − 0.751420I
b = −0.008028 − 1.317420I
−2.12887 − 0.87840I −1.69411 − 0.10409I
u = −0.152365 + 1.192150I
a = −0.893744 + 0.183757I
b = −0.260772 + 0.484211I
−3.95830 − 1.70076I −0.66920 + 3.77891I
u = −0.152365 − 1.192150I
a = −0.893744 − 0.183757I
b = −0.260772 − 0.484211I
−3.95830 + 1.70076I −0.66920 − 3.77891I
u = 1.153410 + 0.362069I
a = −0.124158 − 0.993672I
b = 0.18813 − 1.67407I
−1.52168 − 4.11639I 1.28531 + 7.66399I
u = 1.153410 − 0.362069I
a = −0.124158 + 0.993672I
b = 0.18813 + 1.67407I
−1.52168 + 4.11639I 1.28531 − 7.66399I
u = 0.550134 + 1.176880I
a = −0.727410 + 0.882315I
b = 0.082313 + 0.573084I
6.85248 + 3.47221I 4.05373 − 4.83355I
u = 0.550134 − 1.176880I
a = −0.727410 − 0.882315I
b = 0.082313 − 0.573084I
6.85248 − 3.47221I 4.05373 + 4.83355I
u = −0.450239 + 1.331950I
a = 0.460049 + 0.710367I
b = 0.027730 + 0.522672I
5.01150 + 2.13942I −3.15739 + 7.15620I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.450239 − 1.331950I
a = 0.460049 − 0.710367I
b = 0.027730 − 0.522672I
5.01150 − 2.13942I −3.15739 − 7.15620I
u = 0.290484 + 0.513132I
a = 1.005030 − 0.448330I
b = 0.178104 + 0.233390I
1.086740 + 0.522072I 7.59034 − 2.64068I
u = 0.290484 − 0.513132I
a = 1.005030 + 0.448330I
b = 0.178104 − 0.233390I
1.086740 − 0.522072I 7.59034 + 2.64068I
u = −1.26259 + 0.65120I
a = 0.779025 + 0.806632I
b = 0.89947 + 1.69470I
1.93276 + 4.57399I −0.80312 − 3.71996I
u = −1.26259 − 0.65120I
a = 0.779025 − 0.806632I
b = 0.89947 − 1.69470I
1.93276 − 4.57399I −0.80312 + 3.71996I
u = 1.21341 + 0.77536I
a = −0.786921 + 0.889637I
b = −0.87894 + 1.94262I
4.69053 − 10.38600I 1.88291 + 6.53281I
u = 1.21341 − 0.77536I
a = −0.786921 − 0.889637I
b = −0.87894 − 1.94262I
4.69053 + 10.38600I 1.88291 − 6.53281I
u = −0.72141 + 1.25819I
a = 0.852837 + 0.774968I
b = −0.116207 + 0.690641I
1.18821 − 7.91289I −0.57657 + 4.83516I
u = −0.72141 − 1.25819I
a = 0.852837 − 0.774968I
b = −0.116207 − 0.690641I
1.18821 + 7.91289I −0.57657 − 4.83516I
u = −1.36519 + 0.61368I
a = 0.190407 − 1.118590I
b = −0.07359 − 1.82092I
−7.80864 + 8.10776I −0.12578 − 8.54506I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.36519 − 0.61368I
a = 0.190407 + 1.118590I
b = −0.07359 + 1.82092I
−7.80864 − 8.10776I −0.12578 + 8.54506I
u = −1.22422 + 0.88045I
a = 0.754688 + 0.924811I
b = 0.75841 + 2.06080I
−0.5454 + 15.5229I −1.18119 − 7.76656I
u = −1.22422 − 0.88045I
a = 0.754688 − 0.924811I
b = 0.75841 − 2.06080I
−0.5454 − 15.5229I −1.18119 + 7.76656I
u = −0.435512
a = −0.249742
b = −0.798841
−1.27409 −10.1920
u = 1.55472 + 0.34572I
a = −0.514140 + 0.857873I
b = −0.33875 + 1.54021I
−9.70709 − 4.18623I −3.33842 + 3.07970I
u = 1.55472 − 0.34572I
a = −0.514140 − 0.857873I
b = −0.33875 − 1.54021I
−9.70709 + 4.18623I −3.33842 − 3.07970I
u = −0.372671
a = 4.40350
b = −0.190276
7.09486 −26.8760
7
II. I
u
2
= h1.76 × 10
5
u
14
+ 1.28 × 10
5
u
13
+ · · · + 7.47 × 10
4
b − 9.28 ×
10
5
, 61025u
14
+ 17351u
13
+ · · · + 74749a − 408316, u
15
− 3u
13
+ · · · − 3u + 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
a
12
=
−0.816399u
14
− 0.232124u
13
+ ··· + 2.19719u + 5.46249
−2.35940u
14
− 1.71284u
13
+ ··· − 2.65182u + 12.4181
a
7
=
−4.03019u
14
− 1.09145u
13
+ ··· + 0.200738u + 9.47793
−3.84659u
14
− 1.32358u
13
+ ··· − 1.60207u + 11.9404
a
6
=
−4.03019u
14
− 1.09145u
13
+ ··· + 0.200738u + 9.47793
−4.62779u
14
− 1.33257u
13
+ ··· − 0.846232u + 13.0319
a
10
=
−1.59760u
14
− 0.241114u
13
+ ··· + 2.95303u + 6.55395
−3.18414u
14
− 1.54132u
13
+ ··· − 0.0217260u + 13.7507
a
1
=
0.781201u
14
+ 0.00899009u
13
+ ··· − 0.755836u − 1.09145
0.824733u
14
− 0.171521u
13
+ ··· − 1.63010u − 1.33257
a
11
=
−0.964307u
14
+ 0.388567u
13
+ ··· + 5.09634u + 3.98178
−2.50731u
14
− 1.09215u
13
+ ··· + 0.247321u + 10.9374
a
5
=
0.150290u
14
+ 0.121125u
13
+ ··· + 0.120028u + 0.232124
−0.630911u
14
+ 0.112135u
13
+ ··· + 0.875865u + 1.32358
a
2
=
0.150290u
14
+ 0.121125u
13
+ ··· + 0.120028u + 0.232124
0.599460u
14
+ 0.0788238u
13
+ ··· − 0.662778u − 1.44470
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2294032
74749
u
14
+
1099194
74749
u
13
+ ··· +
2094016
74749
u −
7660470
74749
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
u
15
+ 4u
14
+ ··· − 5u + 1
c
3
u
15
− 3u
13
+ ··· − 3u + 1
c
4
u
15
− 4u
14
+ ··· − 5u − 1
c
5
, c
11
u
15
+ 5u
13
+ ··· − 3u + 1
c
6
, c
12
u
15
+ 3u
14
+ ··· − 5u
2
− 1
c
7
u
15
+ 5u
13
+ ··· − 3u − 1
c
8
u
15
− 3u
13
+ ··· − 3u − 1
c
9
u
15
− 3u
14
+ ··· + 5u
2
+ 1
c
10
u
15
+ 5u
14
+ ··· + 3u
2
+ 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
15
− 14y
14
+ ··· + 21y −1
c
3
, c
8
y
15
− 6y
14
+ ··· + 17y −1
c
5
, c
7
, c
11
y
15
+ 10y
14
+ ··· + 5y −1
c
6
, c
9
, c
12
y
15
− 5y
14
+ ··· − 10y −1
c
10
y
15
− 13y
14
+ ··· − 6y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.395101 + 0.883245I
a = −0.283707 + 0.375012I
b = 0.846671 + 0.071188I
−6.05368 − 0.92102I −7.55931 − 0.86682I
u = −0.395101 − 0.883245I
a = −0.283707 − 0.375012I
b = 0.846671 − 0.071188I
−6.05368 + 0.92102I −7.55931 + 0.86682I
u = −1.16272
a = −1.84176
b = −0.922893
−1.62169 4.25160
u = −0.790290 + 0.123203I
a = 0.852557 + 0.556939I
b = 0.44109 + 2.17069I
−4.81976 + 0.84883I −3.58248 − 7.41027I
u = −0.790290 − 0.123203I
a = 0.852557 − 0.556939I
b = 0.44109 − 2.17069I
−4.81976 − 0.84883I −3.58248 + 7.41027I
u = 0.286985 + 1.190230I
a = 0.329297 − 0.950489I
b = 0.138941 − 0.584308I
5.13698 − 2.55464I 3.03982 + 10.26539I
u = 0.286985 − 1.190230I
a = 0.329297 + 0.950489I
b = 0.138941 + 0.584308I
5.13698 + 2.55464I 3.03982 − 10.26539I
u = 1.049150 + 0.637502I
a = −0.057199 − 0.441891I
b = −0.258968 − 1.198930I
−3.04339 − 2.80173I −4.84923 + 4.43441I
u = 1.049150 − 0.637502I
a = −0.057199 + 0.441891I
b = −0.258968 + 1.198930I
−3.04339 + 2.80173I −4.84923 − 4.43441I
u = 1.326480 + 0.349849I
a = −0.688768 + 0.786265I
b = −0.22129 + 1.79626I
−11.19200 − 3.11061I −6.06432 + 1.93594I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.326480 − 0.349849I
a = −0.688768 − 0.786265I
b = −0.22129 − 1.79626I
−11.19200 + 3.11061I −6.06432 − 1.93594I
u = −1.29612 + 0.71007I
a = 0.051371 − 0.786186I
b = 0.00761 − 1.51725I
−8.56116 + 7.21256I −5.69398 − 4.24135I
u = −1.29612 − 0.71007I
a = 0.051371 + 0.786186I
b = 0.00761 + 1.51725I
−8.56116 − 7.21256I −5.69398 + 4.24135I
u = 0.474863
a = 3.57874
b = 1.81758
3.63405 14.5470
u = 0.325638
a = 4.85593
b = 7.19722
2.41576 −45.3800
12
III. I
u
3
= h4u
7
− 2u
6
+ · · · − 2ba + 7, −u
7
a − 2u
7
+ · · · − 2a − 4, u
8
− u
7
−
u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
u
2
a
8
=
u
u
a
12
=
a
b
a
7
=
−u
7
+ u
6
+ u
5
− 2u
4
+ bau − u
3
+ 2u
2
− a + u − 2
−2u
7
+ 2u
6
− u
3
ba + 2u
5
− 4u
4
+ bau + u
2
a − 3u
3
+ 4u
2
+ 2u − 4
a
6
=
−u
7
+ u
6
+ u
5
− 2u
4
+ bau − u
3
+ 2u
2
− a + u − 2
−2u
7
+ 2u
6
+ 2u
5
− 4u
4
+ bau − 2u
3
+ 4u
2
+ u − 4
a
10
=
−u
4
a − u
2
b + u
2
a + a
−u
4
a − u
2
b + 2u
2
a + b
a
1
=
u
3
u
3
− u
a
11
=
−u
2
b + u
2
a + a
−u
2
b + u
2
a + b
a
5
=
−u
5
− u
−u
5
+ u
3
− u
a
2
=
u
5
+ u
u
7
− u
5
+ 2u
3
− u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
− 4u
4
− 8u
3
+ 4u
2
+ 4u − 6
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
4
c
3
, c
8
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
4
c
5
, c
7
, c
11
u
32
− 3u
31
+ ··· − 168u − 191
c
6
, c
9
, c
12
u
32
+ 3u
31
+ ··· + 202u + 71
c
10
(u
2
− u − 1)
16
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
4
c
3
, c
8
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
4
c
5
, c
7
, c
11
y
32
+ 11y
31
+ ··· − 90108y + 36481
c
6
, c
9
, c
12
y
32
− 21y
31
+ ··· − 309468y + 5041
c
10
(y
2
− 3y + 1)
16
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.570868 + 0.730671I
a = −0.410360 + 0.525233I
b = −1.206890 + 0.200385I
−4.98850 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 + 0.730671I
a = −0.410360 + 0.525233I
b = 0.73898 + 1.30166I
−4.98850 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 + 0.730671I
a = 1.07434 − 1.37508I
b = −0.054189 − 1.226940I
2.90719 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 + 0.730671I
a = 1.07434 − 1.37508I
b = 1.27918 − 2.70546I
2.90719 + 1.13123I 0.584775 − 0.510791I
u = 0.570868 − 0.730671I
a = −0.410360 − 0.525233I
b = −1.206890 − 0.200385I
−4.98850 − 1.13123I 0.584775 + 0.510791I
u = 0.570868 − 0.730671I
a = −0.410360 − 0.525233I
b = 0.73898 − 1.30166I
−4.98850 − 1.13123I 0.584775 + 0.510791I
u = 0.570868 − 0.730671I
a = 1.07434 + 1.37508I
b = −0.054189 + 1.226940I
2.90719 − 1.13123I 0.584775 + 0.510791I
u = 0.570868 − 0.730671I
a = 1.07434 + 1.37508I
b = 1.27918 + 2.70546I
2.90719 − 1.13123I 0.584775 + 0.510791I
u = −0.855237 + 0.665892I
a = 0.449903 + 0.350297I
b = −0.005773 + 1.352800I
−1.78843 + 2.57849I 3.72292 − 3.56796I
u = −0.855237 + 0.665892I
a = 0.449903 + 0.350297I
b = 0.377013 − 0.240663I
−1.78843 + 2.57849I 3.72292 − 3.56796I
16
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855237 + 0.665892I
a = −1.17786 − 0.91709I
b = 0.197214 − 0.794544I
6.10726 + 2.57849I 3.72292 − 3.56796I
u = −0.855237 + 0.665892I
a = −1.17786 − 0.91709I
b = −1.16913 − 2.11707I
6.10726 + 2.57849I 3.72292 − 3.56796I
u = −0.855237 − 0.665892I
a = 0.449903 − 0.350297I
b = −0.005773 − 1.352800I
−1.78843 − 2.57849I 3.72292 + 3.56796I
u = −0.855237 − 0.665892I
a = 0.449903 − 0.350297I
b = 0.377013 + 0.240663I
−1.78843 − 2.57849I 3.72292 + 3.56796I
u = −0.855237 − 0.665892I
a = −1.17786 + 0.91709I
b = 0.197214 + 0.794544I
6.10726 − 2.57849I 3.72292 + 3.56796I
u = −0.855237 − 0.665892I
a = −1.17786 + 0.91709I
b = −1.16913 + 2.11707I
6.10726 − 2.57849I 3.72292 + 3.56796I
u = −1.09818
a = 0.562781
b = 0.22342 + 1.55964I
−10.4506 −5.86400
u = −1.09818
a = 0.562781
b = 0.22342 − 1.55964I
−10.4506 −5.86400
u = −1.09818
a = −1.47338
b = −0.894458
−2.55489 −5.86400
u = −1.09818
a = −1.47338
b = −0.275409
−2.55489 −5.86400
17
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.031810 + 0.655470I
a = 1.117270 − 0.709761I
b = −0.349632 − 0.574285I
1.56816 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 + 0.655470I
a = 1.117270 − 0.709761I
b = 0.91467 − 1.90581I
1.56816 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 + 0.655470I
a = −0.426759 + 0.271105I
b = 0.010873 − 0.550359I
−6.32752 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 + 0.655470I
a = −0.426759 + 0.271105I
b = −0.22670 + 1.49767I
−6.32752 − 6.44354I −1.42845 + 5.29417I
u = 1.031810 − 0.655470I
a = 1.117270 + 0.709761I
b = −0.349632 + 0.574285I
1.56816 + 6.44354I −1.42845 − 5.29417I
u = 1.031810 − 0.655470I
a = 1.117270 + 0.709761I
b = 0.91467 + 1.90581I
1.56816 + 6.44354I −1.42845 − 5.29417I
u = 1.031810 − 0.655470I
a = −0.426759 − 0.271105I
b = 0.010873 + 0.550359I
−6.32752 + 6.44354I −1.42845 − 5.29417I
u = 1.031810 − 0.655470I
a = −0.426759 − 0.271105I
b = −0.22670 − 1.49767I
−6.32752 + 6.44354I −1.42845 − 5.29417I
u = 0.603304
a = −1.02442
b = −0.83799 + 2.18510I
−4.79288 −3.89450
u = 0.603304
a = −1.02442
b = −0.83799 − 2.18510I
−4.79288 −3.89450
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.603304
a = 2.68196
b = 0.939976
3.10281 −3.89450
u = 0.603304
a = 2.68196
b = 3.44777
3.10281 −3.89450
19
IV. I
v
1
= ha, 4b − v + 4, v
2
− 6v + 4i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
8
=
v
0
a
12
=
0
1
4
v − 1
a
7
=
v
0.5
a
6
=
−2v + 2
0.5
a
10
=
6v − 4
−
1
4
v
a
1
=
5v − 4
−1
a
11
=
−2v + 2
1
4
v − 1
a
5
=
−5v + 4
1
a
2
=
5v − 3
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
45
8
v
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
c
3
, c
8
u
2
c
4
(u + 1)
2
c
5
, c
7
, c
10
u
2
− u − 1
c
6
u
2
+ 3u + 1
c
9
, c
12
u
2
− 3u + 1
c
11
u
2
+ u − 1
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
8
y
2
c
5
, c
7
, c
10
c
11
y
2
− 3y + 1
c
6
, c
9
, c
12
y
2
− 7y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.763932
a = 0
b = −0.809017
−0.657974 4.29710
v = 5.23607
a = 0
b = 0.309017
7.23771 29.4530
23
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
4
· (u
15
+ 4u
14
+ ··· − 5u + 1)(u
27
− 3u
26
+ ··· − 36u + 16)
c
3
u
2
(u
8
− u
7
+ ··· + 2u − 1)
4
(u
15
− 3u
13
+ ··· − 3u + 1)
· (u
27
+ 5u
26
+ ··· + 400u + 64)
c
4
(u + 1)
2
(u
8
− u
7
− 3u
6
+ 2u
5
+ 3u
4
− 2u − 1)
4
· (u
15
− 4u
14
+ ··· − 5u − 1)(u
27
− 3u
26
+ ··· − 36u + 16)
c
5
(u
2
− u − 1)(u
15
+ 5u
13
+ ··· − 3u + 1)(u
27
+ u
26
+ ··· − 5u − 1)
· (u
32
− 3u
31
+ ··· − 168u − 191)
c
6
(u
2
+ 3u + 1)(u
15
+ 3u
14
+ ··· − 5u
2
− 1)(u
27
− 25u
25
+ ··· + 6u + 1)
· (u
32
+ 3u
31
+ ··· + 202u + 71)
c
7
(u
2
− u − 1)(u
15
+ 5u
13
+ ··· − 3u − 1)(u
27
+ u
26
+ ··· − 5u − 1)
· (u
32
− 3u
31
+ ··· − 168u − 191)
c
8
u
2
(u
8
− u
7
+ ··· + 2u − 1)
4
(u
15
− 3u
13
+ ··· − 3u − 1)
· (u
27
+ 5u
26
+ ··· + 400u + 64)
c
9
(u
2
− 3u + 1)(u
15
− 3u
14
+ ··· + 5u
2
+ 1)(u
27
− 25u
25
+ ··· + 6u + 1)
· (u
32
+ 3u
31
+ ··· + 202u + 71)
c
10
((u
2
− u − 1)
17
)(u
15
+ 5u
14
+ ··· + 3u
2
+ 1)
· (u
27
+ 19u
26
+ ··· − 768u + 256)
c
11
(u
2
+ u − 1)(u
15
+ 5u
13
+ ··· − 3u + 1)(u
27
+ u
26
+ ··· − 5u − 1)
· (u
32
− 3u
31
+ ··· − 168u − 191)
c
12
(u
2
− 3u + 1)(u
15
+ 3u
14
+ ··· − 5u
2
− 1)(u
27
− 25u
25
+ ··· + 6u + 1)
· (u
32
+ 3u
31
+ ··· + 202u + 71)
24
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
4
· (y
15
− 14y
14
+ ··· + 21y − 1)(y
27
− 23y
26
+ ··· − 2192y − 256)
c
3
, c
8
y
2
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
4
· (y
15
− 6y
14
+ ··· + 17y − 1)(y
27
− 9y
26
+ ··· + 49920y − 4096)
c
5
, c
7
, c
11
(y
2
− 3y + 1)(y
15
+ 10y
14
+ ··· + 5y − 1)(y
27
+ 5y
26
+ ··· + 15y − 1)
· (y
32
+ 11y
31
+ ··· − 90108y + 36481)
c
6
, c
9
, c
12
(y
2
− 7y + 1)(y
15
− 5y
14
+ ··· − 10y − 1)(y
27
− 50y
26
+ ··· + 68y − 1)
· (y
32
− 21y
31
+ ··· − 309468y + 5041)
c
10
((y
2
− 3y + 1)
17
)(y
15
− 13y
14
+ ··· − 6y − 1)
· (y
27
− 19y
26
+ ··· + 5636096y − 65536)
25
